2-5 Reason Using Properties from Algebra

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2-5 Reason Using Properties from Algebra
Hubarth Geometry
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Key Concepts Algebraic Properties of
Equality Let a, b, and c be real
numbers. Addition Property If a b, then a c
b c Subtraction Property If a b, then a
c b c Multiplication Property If a b, then
ac bc Division Property If a b, and
Substitution Property If a b, then a can be
substituted for b in any equation or
expression
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Ex 1 Write reasons for Each Step
Solve 2x 5 20 3x. Write a reason for each
step.
2x 5 20 3x
Write original equation.
Given
2x 5 3x 20 3x 3x
Add 3x to each side.
Addition Property of Equality
5x 5 20
Combine like terms.
Simplify.
Subtract 5 from each side.
5x 15
Subtraction Property of Equality
x 3
Divide each side by 5.
Division Property of Equality
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Key Concepts Distributive Property a(b c) ab
ac, where a, b, and c are real numbers.
Ex 2 Use the Distributive Property
Solve -4(11x 2) 80. Write a reason for each
step.
4(11x 2) 80
Write original equation.
Given
44x 8 80
Multiply.
Distributive Property
44x 88
Add 8 to each side.
Addition Property of Equality
x 2
Divide each side by 44.
Division Property of Equality
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Key Concept Reflexive Property of Equality Real
Numbers For any real numbers a, a a Segment
Length For any segment AB, AB AB Angle
Measures For any angle A, Symmetric Property
of Equality Real Numbers For any real number a
and b, if a b, the b a Segment Length For
any segment AB and CD, if AB CD, the CD
AB Angle Measure For any angles A and B,
if Transitive Property of Equality Real
Numbers For any real number a, b, and c, if a
b and b c, then a c Segment Length For any
segments AB, CD and EF, if AB CD and CD EF,
then AB EF Angle Measure For any angles,
A, B, and C, if
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Ex 3 Use Properties of Equality
Marked in diagram.
Given
Add measures of adjacent angles.
Angle Addition Postulate
Substitution Property of Equality
Angle Addition Postulate
Add measures of adjacent angles
Transitive Property of Equality
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Ex 4 Use Properties of Equalities
AB CD
Marked in diagram.
Given
Segment Addition Postulate
AC AB BC
Add lengths of adjacent segments.
BD BC CD
Add lengths of adjacent segments.
Segment Addition Postulate
Addition Property of Equality
Add BC to each side of AB CD.
AB BC CD BC
Substitution Property of Equality
Substitute AC for AB BC and BD for BC CD.
AC BD